Abstract
This chapter studies the problem of finite frequency (FF) H-infinity filtering for continuous-time systems with a constant state delay. The FF specification is motivated by the fact that many practical signals have their energy within an FF range, while the standard H-infinity filter theory cannot directly handle this fact. Using the generalized Kalman-Yakubovich-Popov lemma and the Projection Lemma, delay-dependent and delay-independent FF bounded real lemmas (BRLs) in terms of linear matrix inequalities (LMIs) are proposed for FF H-infinity filtering performance analysis. To prove these BRLs, a frequency-domain proof based on the transfer function representation and a time-domain proof using the Lyapunov-Krasovskii method are presented, respectively. Based on the obtained BRLs, delay-dependent and delay-independent approaches in terms of LMIs are proposed for designing filters with a guaranteed FF H-infinity performance for continuous-time systems with a state delay. What’s more, the delay-partitioning idea is made use of to reduce the conservatism of the delay-dependent approach. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the filter design methods developed in the chapter.
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Notes
- 1.
MATLAB\(^\circledR \) is a registered trademark of The MathWorks, Inc.
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Gao, H., Li, X. (2014). Finite Frequency \(H_{\infty }\) Filtering for Time-Delay Systems. In: Robust Filtering for Uncertain Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-05903-7_8
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DOI: https://doi.org/10.1007/978-3-319-05903-7_8
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